what is the solution set to the following system?
x+y=5
x^2+y^2=25

Question

what is the solution set to the following system?
x+y=5
x^2+y^2=25

anonymous · Answer

(0,-5) (-5,0)
(0,5) (-5,0)
(0,-5) (5,0)
(0,5) (5,0)

mathmale · Answer

What have YOU thought of doing so far?
As for me, I'd use SUBSTITUTION to solve this problem.  Soplve the first equation for either x or y in terms of the other variable.  Substitute the resulting expression into the 2nd equation.

anonymous · Answer

alright so x-y=5 would be y=5-x
I then would plug this into x^2+y^2=25 right?
so x^2 + (5-x)^2=25
yeah?

anonymous · Answer

x^2+5-x^2=25
....?

mathmale · Answer

Nice work!$$x^2 + (5-x)^2=25\rightarrow x ^{2}+25-10x+x ^{2}=25.$$Solve for x.  Once you have x, calculate y.  Be certain to check all possibilities, positive and negative.

mathmale · Answer

Be careful:  x^2 + (5-x)^2=25 does not result in x^2+5-x^2 = 25.

anonymous · Answer

ok so would this come out to be 2x^2 +25 -10x after adding like terms?
that cant be right!